The time it will take for your bursitis in your hip to heal will depend on the actual cause of the bursitis in the hip.
In my experience though when I had bursitis in my hip a few years ago it took me a little over 6 weeks to fully recover from the bursitis in the hip and for it to heal.
If the bursitis in your hip hasn't healed within 3 months time then a doctors visit should be scheduled because bursitis in the hip shouldn't last longer than 2 to 3 months.